We present in Fig. REF  the one-dimensional
likelihood functions for the ratios of supersymmetric SU(5) and SM predictions
for the BRs of \(h \rightarrow \gamma \gamma \)  (left panel), \(h \rightarrow Z Z^*\)  (middle panel) The
likelihood function for \(h \rightarrow W W^*\)  is very similar to that for \(h \rightarrow Z Z^*\) , because of
custodial symmetry. and \(h \rightarrow gg\)  decays (right panel). We see that in
each case the
preferred region in the fit corresponds to a prediction in the
SU(5) model that deviates from the SM case by at most a few %, whereas
the present experimental uncertainties in the different coupling
modifiers (employing some theory assumptions) are typically
\({\cal O}(30)\) % [1]}, and a precision of
\({\cal O}(5-10\%)\)  (with the same theory assumptions) can be reached by
the end of the LHC programme.
On the other hand, future \(e^+e^-\)  colliders such as the ILC, CLIC or
FCC-ee anticipate a precision at the percent level for couplings to
fermions and at the permille level for couplings to massive gauge
bosons [2]}, [3]}. This offers the
possiblity that deviations from the SM in the SUSY SU(5) GUT model can
be measured in the future.
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